""" Heavy Tails Animation for @fminxyz Telegram Channel 1080x1080 px, 12 fps, 25 seconds (= 300 frames) Three acts: Act 1 (0-8s): PDF comparison: Gaussian vs Cauchy Act 2 (8-16s): Sampling animation with outliers Act 3 (16-25s): Log-log power law plot """ import os import sys import tempfile import subprocess import numpy as np import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from matplotlib.lines import Line2D from scipy import stats import warnings warnings.filterwarnings('ignore') OUTPUT = "/root/Strategy/content/drafts/heavy_tails_animation.mp4" FPS = 12 DUR = 25 NFRAM = FPS * DUR # 300 DPI = 100 FW, FH = 10.8, 10.8 BG = "#1a1a2e" PAN = "#16213e" CYAN = "#00d4ff" PINK = "#ff6b9d" TXT = "#e8e8f0" ACC = "#a8a8ff" GRD = "#2a2a4a" YELL = "#ffe066" rng = np.random.default_rng(42) x_pdf = np.linspace(-8, 8, 400) gauss_pdf = stats.norm.pdf(x_pdf, 0, 1) cauchy_pdf = stats.cauchy.pdf(x_pdf, 0, 1) x_tail = np.linspace(2.5, 8, 150) gauss_tail = stats.norm.pdf(x_tail, 0, 1) cauchy_tail = stats.cauchy.pdf(x_tail, 0, 1) N_S = 140 gauss_s = rng.standard_normal(N_S) cauchy_s = rng.standard_cauchy(N_S) x_ll = np.logspace(0, 4, 100) pareto_ccdf = x_ll ** (-1.5) exp_ccdf = np.exp(-x_ll / 150) A1S, A1E = 0, 8 * FPS # 0..96 A2S, A2E = 8 * FPS, 16 * FPS # 96..192 A3S, A3E = 16 * FPS, NFRAM # 192..300 BLEND = 5 def cl(v, lo=0.0, hi=1.0): return float(max(lo, min(hi, v))) def fp(local, s, e, dur): a = s * dur; b = e * dur return cl((local - a) / max(1, b - a)) def make_frame(frame, fig, axes): ax1, ax1t, ax2g, ax2h, ax3, axT, axB = axes fig.patch.set_facecolor(BG) def hide(): for a in [ax1, ax1t, ax2g, ax2h, ax3]: a.set_visible(False); a.cla() for a in [axT, axB]: a.cla(); a.axis('off') a.set_xlim(0, 1); a.set_ylim(0, 1) def sty(ax, xl='', yl='', ti=''): ax.set_facecolor(PAN) ax.tick_params(colors=TXT, labelsize=10) for sp in ax.spines.values(): sp.set_color(GRD) if xl: ax.set_xlabel(xl, fontsize=11, color=TXT) if yl: ax.set_ylabel(yl, fontsize=11, color=TXT) if ti: ax.set_title(ti, fontsize=13, color=TXT, pad=5) ax.grid(True, color=GRD, alpha=0.35, linewidth=0.5) # ── ACT 1 ────────────────────────────────────────────────────────────────── def act1(f): lf = f - A1S dur = A1E - A1S hide() ax1.set_visible(True) sty(ax1, xl='x', yl='PDF(x)') ax1.set_xlim(-6.5, 6.5) ax1.set_ylim(-0.01, 0.42) fg = fp(lf, 0.00, 0.38, dur) ng = max(2, int(fg * len(x_pdf))) ax1.plot(x_pdf[:ng], gauss_pdf[:ng], color=CYAN, lw=2.5, zorder=3) fc = fp(lf, 0.22, 0.60, dur) nc = max(2, int(fc * len(x_pdf))) ax1.plot(x_pdf[:nc], cauchy_pdf[:nc], color=PINK, lw=2.5, zorder=3) ft = fp(lf, 0.52, 0.82, dur) if ft > 0: mask = x_pdf > 2.5 ax1.fill_between(x_pdf[mask], 0, gauss_pdf[mask], color=CYAN, alpha=ft * 0.20) ax1.fill_between(x_pdf[mask], 0, cauchy_pdf[mask], color=PINK, alpha=ft * 0.30) fa = fp(lf, 0.68, 1.00, dur) if fa > 0.05: ax1.annotate("Тяжёлый хвост", xy=(4.0, stats.cauchy.pdf(4.0)), xytext=(3.1, 0.05 + 0.13 * fa), fontsize=12, color=PINK, fontweight='bold', alpha=fa, arrowprops=dict(arrowstyle='->', color=PINK, lw=1.5, connectionstyle='arc3,rad=-0.2')) ax1.annotate("Лёгкий хвост", xy=(3.0, stats.norm.pdf(3.0)), xytext=(2.0, 0.12 + 0.12 * fa), fontsize=12, color=CYAN, alpha=fa, arrowprops=dict(arrowstyle='->', color=CYAN, lw=1.5, connectionstyle='arc3,rad=0.2')) fz = fp(lf, 0.75, 1.00, dur) ax1t.set_visible(fz > 0.05) if fz > 0.05: sty(ax1t, ti='Хвост (x > 2.5)') ax1t.set_facecolor('#0d0d1f') ax1t.set_xlim(2.5, 7.5) ax1t.set_ylim(-0.003, 0.075) for sp in ax1t.spines.values(): sp.set_color(PINK); sp.set_linewidth(1.8) nt = max(2, int(fz * len(x_tail))) ax1t.plot(x_tail[:nt], gauss_tail[:nt], color=CYAN, lw=2, alpha=0.9) ax1t.plot(x_tail[:nt], cauchy_tail[:nt], color=PINK, lw=2, alpha=0.9) ax1t.fill_between(x_tail[:nt], 0, cauchy_tail[:nt], color=PINK, alpha=0.25) if fc > 0.3: legs = [Line2D([0],[0], color=CYAN, lw=2.5, label='Гауссовское N(0,1)'), Line2D([0],[0], color=PINK, lw=2.5, label='Коши (тяжёлый хвост)')] ax1.legend(handles=legs, loc='upper left', fontsize=11, facecolor='#0d0d20', edgecolor=GRD, labelcolor=TXT) fa0 = fp(lf, 0.00, 0.18, dur) axT.text(0.5, 0.55, 'Тяжёлые хвосты', ha='center', va='center', fontsize=30, fontweight='bold', color=TXT, alpha=fa0) axT.text(0.5, 0.12, 'Heavy Tails', ha='center', va='center', fontsize=16, color=ACC, alpha=fa0 * 0.8) axB.text(0.5, 0.6, 'Функция плотности вероятности', ha='center', va='center', fontsize=14, color=ACC, alpha=fp(lf, 0.08, 0.28, dur)) # ── ACT 2 ────────────────────────────────────────────────────────────────── def act2(f): lf = f - A2S dur = A2E - A2S hide() ax2g.set_visible(True); ax2h.set_visible(True) sty(ax2g, xl='Сэмпл №', yl='Значение', ti='Гауссовское N(0,1)') sty(ax2h, xl='Сэмпл №', yl='', ti='Коши (тяжёлый хвост)') YR = 22 for ax in [ax2g, ax2h]: ax.set_xlim(0, N_S); ax.set_ylim(-YR, YR) ax.axhline(0, color=GRD, lw=0.8) n = min(N_S, max(0, int(fp(lf, 0.00, 0.88, dur) * N_S))) if n > 0: xs = np.arange(n) gv = gauss_s[:n] cv = np.clip(cauchy_s[:n], -YR*1.5, YR*1.5) ax2g.scatter(xs, gv, c=CYAN, s=14, alpha=0.7, zorder=3) cc = [YELL if abs(cauchy_s[i]) > 8 else PINK for i in range(n)] ax2h.scatter(xs, cv, c=cc, s=14, alpha=0.7, zorder=3) if n > 1: ax2g.plot(xs, gv, color=CYAN, alpha=0.18, lw=0.6) ax2h.plot(xs, np.clip(cauchy_s[:n], -YR, YR), color=PINK, alpha=0.18, lw=0.6) n_out = int(np.sum(np.abs(cauchy_s[:n]) > 8)) if n > 0 else 0 fa_o = fp(lf, 0.35, 0.58, dur) if n_out > 0 and fa_o > 0: ax2h.text(0.97, 0.96, f'Выбросов: {n_out}', transform=ax2h.transAxes, ha='right', va='top', fontsize=14, color=YELL, fontweight='bold', alpha=fa_o) if n > 15: fa_s = fp(lf, 0.45, 0.68, dur) if fa_s > 0: ax2g.text(0.97, 0.96, f'σ ≈ {np.std(gauss_s[:n]):.2f}', transform=ax2g.transAxes, ha='right', va='top', fontsize=14, color=CYAN, fontweight='bold', alpha=fa_s) ab = fp(lf, 0.28, 0.55, dur) * 0.12 ax2g.axhspan(-2, 2, color=CYAN, alpha=ab) fa_b = fp(lf, 0.42, 0.62, dur) if fa_b > 0: ax2g.text(1.5, 2.5, '±2σ = 95%', fontsize=10, color=CYAN, alpha=fa_b) fa0 = fp(lf, 0.00, 0.15, dur) axT.text(0.5, 0.55, 'Сэмплирование', ha='center', va='center', fontsize=30, fontweight='bold', color=TXT, alpha=fa0) axB.text(0.5, 0.6, 'Тяжёлые хвосты = экстремальные выбросы', ha='center', va='center', fontsize=14, color=PINK, alpha=fa0) # ── ACT 3 ────────────────────────────────────────────────────────────────── def act3(f): lf = f - A3S dur = A3E - A3S hide() ax3.set_visible(True) sty(ax3, xl='x (log scale)', yl='P(X > x) (log scale)', ti='Степенной закон = прямая линия в log-log') ax3.set_xscale('log'); ax3.set_yscale('log') ax3.set_xlim(1, 15000); ax3.set_ylim(5e-6, 2.0) p1 = fp(lf, 0.00, 0.42, dur) n1 = max(2, int(p1 * len(x_ll))) ax3.plot(x_ll[:n1], exp_ccdf[:n1], color=CYAN, lw=2.5) p2 = fp(lf, 0.25, 0.70, dur) n2 = max(2, int(p2 * len(x_ll))) ax3.plot(x_ll[:n2], pareto_ccdf[:n2], color=PINK, lw=3.0) p3 = fp(lf, 0.60, 0.88, dur) if p3 > 0.01: ax3.text(0.60, 0.72, 'Наклон = −α = −1.5', transform=ax3.transAxes, fontsize=14, color=PINK, fontweight='bold', alpha=p3, bbox=dict(boxstyle='round,pad=0.4', facecolor='#1a0020', edgecolor=PINK, alpha=p3 * 0.7)) anns = [(200, "Частоты слов\n(Закон Ципфа)", 0.55), (1500, "Распределение\nбогатства", 0.68), (8000, "Scaling Laws\nнейросетей", 0.80)] for xi, label, sf in anns: pa = fp(lf, sf, sf + 0.18, dur) if pa > 0.01: yi = xi ** (-1.5) ax3.annotate(label, xy=(xi, yi), xytext=(xi * 1.8, yi * 5), fontsize=11, color=ACC, fontweight='bold', alpha=pa, arrowprops=dict(arrowstyle='->', color=ACC, lw=1.2, connectionstyle='arc3,rad=0.15'), bbox=dict(boxstyle='round,pad=0.3', facecolor='#0d0d25', edgecolor=ACC, alpha=pa * 0.8)) if p2 > 0.3: fa = fp(lf, 0.45, 0.65, dur) legs = [Line2D([0],[0], color=CYAN, lw=2.5, label='Экспоненциальный (лёгкий)'), Line2D([0],[0], color=PINK, lw=3.0, label='Степенной закон (тяжёлый)')] ax3.legend(handles=legs, loc='lower left', fontsize=11, facecolor='#0d0d20', edgecolor=GRD, labelcolor=TXT, framealpha=max(0, fa)) fa0 = fp(lf, 0.00, 0.16, dur) axT.text(0.5, 0.55, 'Реальный мир', ha='center', va='center', fontsize=30, fontweight='bold', color=TXT, alpha=fa0) axB.text(0.5, 0.6, 'Тяжёлые хвосты повсюду в ML и природе', ha='center', va='center', fontsize=14, color=ACC, alpha=fa0) # ── dispatch ─────────────────────────────────────────────────────────────── if frame < A1E - BLEND: act1(frame) elif frame < A2S + BLEND: act1(frame) if (frame - (A1E - BLEND)) < BLEND else act2(frame) elif frame < A2E - BLEND: act2(frame) elif frame < A3S + BLEND: act2(frame) if (frame - (A2E - BLEND)) < BLEND else act3(frame) else: act3(frame) def main(): tmpdir = tempfile.mkdtemp(prefix='ht_') print(f"Rendering {NFRAM} frames ({DUR}s @ {FPS}fps) → {tmpdir}") fig = plt.figure(figsize=(FW, FH), dpi=DPI, facecolor=BG) ax1 = fig.add_axes([0.09, 0.17, 0.86, 0.64]) ax1t = fig.add_axes([0.60, 0.38, 0.31, 0.31]) ax2g = fig.add_axes([0.07, 0.17, 0.41, 0.64]) ax2h = fig.add_axes([0.54, 0.17, 0.41, 0.64]) ax3 = fig.add_axes([0.10, 0.14, 0.84, 0.70]) axT = fig.add_axes([0.0, 0.86, 1.0, 0.12], facecolor='none') axT.set_xlim(0,1); axT.set_ylim(0,1); axT.axis('off') axB = fig.add_axes([0.0, 0.00, 1.0, 0.15], facecolor='none') axB.set_xlim(0,1); axB.set_ylim(0,1); axB.axis('off') axes = (ax1, ax1t, ax2g, ax2h, ax3, axT, axB) for i in range(NFRAM): make_frame(i, fig, axes) fig.savefig(os.path.join(tmpdir, f"f{i:04d}.png"), facecolor=BG, dpi=DPI) if i % 30 == 0: print(f" {i}/{NFRAM}", flush=True) plt.close(fig) print("Encoding with ffmpeg ...") cmd = ['ffmpeg', '-y', '-framerate', str(FPS), '-i', os.path.join(tmpdir, 'f%04d.png'), '-c:v', 'libx264', '-preset', 'fast', '-crf', '20', '-pix_fmt', 'yuv420p', '-movflags', '+faststart', OUTPUT] r = subprocess.run(cmd, capture_output=True, text=True) if r.returncode != 0: print("ffmpeg error:\n", r.stderr[-2000:]) sys.exit(1) import shutil; shutil.rmtree(tmpdir) size_mb = os.path.getsize(OUTPUT) / 1e6 print(f"Done! {OUTPUT} ({size_mb:.1f} MB)") if __name__ == '__main__': main()